How do you divide #\frac { 4} { 3} \div \frac { 2} { 15}#?

2 Answers
Dec 2, 2016

#10#

Explanation:

#4/3 -: 2/15 = 20/15 -: 2/15#

#20/15 -: 2/15 = 150/15#

#150/15 = 10#

Dec 4, 2016

10

#color(red)("Several way of doing this calculation type")#

Explanation:

Write #4/3-:2/15" as "4/3xx15/2#

#color(blue)(4/3)xx color(green)(15/2)" is the same as "color(blue)(4/(color(green)(2))xx(color(green)(15))/3) = 2xx5=10 #

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Or you can do it this way:

#(cancel(4)^2)/(cancel(3)^1)xx(cancel(15)^5)/(cancel(2)^1) = 2xx5 =10#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Or you can do it this way:

A fraction consists of: #" "("count")/("size indicator") -> ("numerator")/("denominator")#

#color(white)(.)#

#color(green)([4/3color(red)(xx1)] -:2/15" "->" "[4/3color(red)(xx5/5)] -:2/15#

#" "[20/15]-:2/15#

As the bottom numbers (size indicators -> denominators) are the same then you can do this:

#" "color(magenta)(20/15-:2/15" gives the same answer as " 20 -:2 = 10)#

#color(green)("You can only directly add, subtract or divide the counts if the size indicators are the same")#

This is why you can do #6-:3# directly. They are in fact #6/1-:3/1# so their size indicators are the same.

People do not normally write the whole numbers this way. However, not writing it does not mean that it is not there.